We model the elastic forces \({f}_\text{el}\)  according to the Euler-Bernoulli beam theory which takes into account only the local curvature of the filament and the longitudinal tension [1]}, [2]}. The elastic force density is then given by
\({f}_\textnormal {el} = EI\,\partial _{ssss}{x} - \partial _s (T(s) \partial _s{x}),\) 
